One way to help with chicken winging is to concentrate, not necessarily on keeping your elbow straight, but pointing it towards tour body. When you keep your elbow in, there's no way you can get your hand around the ball, thus keeping it behind the ball where you want it. Keeping your elbow completely straight is not a necessity in bowling; it might actually hinder your game a bit because it could throw you off balance. Also, when your elbow is completely straight, you are relying completely on the strength of your wrist to hold the ball in position, which could cause injury (depending on what weight you throw).
Also, another thing that could cause getting around the ball would be slumping forward. If you aren't upright at the foul line, then your hand will most likely rotate around the ball. You can see even just standing up right where you are. Stand up and see where your hand is, then slump forward and you'll notice that it turns in toward your body. Keeping upright also requires a very steady head. If you jerk your head at the end of your approach, then you'll probably get around the ball. Keeping your head steady will not only help you stay balanced, work the inside of the ball, and keep you upright, it will also make you much more accurate.
Try this. Fold up a towel to maybe 6" by 6" or so and place it on the top of your head. Throw a ball, and if the towel flies off, then you're jerking your head. This is a really easy practice tool; you may look like an idiot, but you'll end up being the one throwing more strikes (and spares too).